I've never used no-ip so I'm not sure, but I'd imagine that you run the client software on your server. This runs all the time and monitors your external IP address. Whenever this changes, it should notify no-ip and let them know about the IP change. They should then update your A record (do they give you username.no-ip.com or something similar?) so that the subdomain always points to your actual external IP. Then, the remote clients should just be able to use this subdomain (rather than specifiying an actual IP address) to connect to your server.

I've never used no-ip so I'm not sure, but I'd imagine that you run the client software on your server. This runs all the time and monitors your external IP address. Whenever this changes, it should notify no-ip and let them know about the IP change. They should then update your A record (do they give you username.no-ip.com or something similar?) so that the subdomain always points to your actual external IP. Then, the remote clients should just be able to use this subdomain (rather than specifiying an actual IP address) to connect to your server.